Game theory
Game theory is the study of how optimal strategies are formulated in conflict. It is concerned with the requirement of decision making in situations where two or more rational opponents are involved under conditions of competition and conflicting interests in anticipation of certain outcomes over a period of time. You are surely aware of the fact that in a competitive environment the strategies taken by the opponent organizations or individuals can dramatically affect the outcome of a particular decision by an organization. In the automobile industry, for example, the strategies of competitors to introduce certain models with certain features can dramatically affect the profitability of other carmakers. So, in order to make important decisions in business, it is necessary to consider what other organizations or individuals are doing or might do. Game theory is a way to consider the impact of the strategies of one, on the strategies and outcomes of the other. In this you will determine the rules of rational behavior in the game situations, in which the outcomes are dependent on the actions of the interdependent players.
A GAME refers to a situation in which two or more players are competing. It involves the players (decision makers) who have different goals or objectives. They are in a situation in which there may be a number of possible outcomes with different values to them. Although they might have some control that would influence the outcome, they do not have complete control over others. Unions striking against the company management, players in a chess game, firm striving for larger share of market are a few illustrations that can be viewed as games.
Game Theory Strategy may be of two types:
- Pure strategy - If the players select the same strategy each time, then it is referred as pure – strategy. In this case each player knows exactly what the opponent is going to do and the objective of the players is to maximize gains or to minimize losses.
- Mixed Strategy - When the players use a combination of strategies with some fixed probabilities and each player kept guessing as to which course of action is to be selected by the other player at a particular occasion then this is known as mixed strategy. Thus, there is probabilistic situation and objective of the player is to maximize expected gains or to minimize losses strategies. Mixed strategy is a selection among pure strategies with fixed probabilities.
Simulation
What is Simulation?
Simulation means imitation of reality. The purpose of simulation in the business world is to understand the behavior of a system. Before making many important decisions, we simulate the result to insure that we are doing the right thing.
Simulation is used under two conditions.
- First, when experimentation is not possible. Note that if we can do a real experiment, the results would obviously be better than simulation.
- Second condition for using simulation is when the analytical solution procedure is not known. If analytical formulas are known then we can find the actual expected value of the results quickly by using the formulas. In simulation we can hope to get the same results after simulating thousands of times.
Why Simulation?
This is a fundamental and quantitative way to understand complex systems/phenomena which is complementary to the traditional approaches of theory and experiment. Simulation is concerned with powerful methods of analysis designed to exploit high performance computing. This approach is becoming increasingly widespread in basic research and advanced technological applications, cross cutting the fields of physics, chemistry, mechanics, engineering, and biology
Advantage of Simulation
- relative straight forward
- can solve large, complex problems
- allows "what if" questions
- Does not interfere with real world systems
- allows study of interactive variables
- allows time compression
- allows inclusion of real-world complication
Disadvantage of simulation
- require generation of all condition and constraints of real-world problem
- each model is unique
- often require long expensive process
- does not generate optimal solutions
Monte Carlo method of Simulation
The Monte Carlo method owes its development to the two mathematicians, John Von Neumann and Stanislaw Ulam, during World War II. The principle behind this method of simulation is representative of the given system under analysis by a system described by some known probability distribution and then drawing random samples for probability distribution by means of random number. In case it is not possible to describe a system in terms of Standard probability distribution such as normal, Poisson, exponential, gamma, etc., an empirical probability distribution can be constructed.
The deterministic method of simulation cannot always be applied to complex real-life situations due to inherently high cost and time values required so as to obtain any meaningful results from the simulated model. Since there are a large number of interactions between numerous variables, the system becomes too complicated to offer an effective simulation approach. In such cases where it is not feasible to use an expectation approach for simulating systems, Monte Carlo method of simulation is used. It can be usefully applied in cases where the system to be simulated has a large number of elements that exhibit chance (probability) in their behaviour. As already mentioned, the various types of probability distributions are used to represent the uncertainty of real-life situations in the model.
Simulation is normally undertaken only with the help of a very high-speed data processing machine such as computer. The user of simulation technique must always bear in mind that the actual frequency or probability would approximate the theoretical value of probability only when the number of trials is very large i.e. when the simulation is repeated a large no. of times. This can easily be achieved with the help of a computer by generating random numbers
Following are the steps involved in Monte-Carlo simulation: -
- Step I. - Obtain the frequency or probability of all the important variables from the historical sources.
- Step II. - Convert the respective probabilities of the various variables into cumulative problems.
- Step III. - Generate random numbers for each such variable.
- Step IV. - Based on the cumulative probability distribution table obtained in Step II, obtain the interval (i.e.; the range) of the assigned random numbers.
- Step V. - Simulate a series of experiments or trails.
Remarks. Which random number to use?
Random Number Generation
A random number generator (often abbreviated as RNG) is a computational or physical device designed to generate a sequence of numbers or symbols that lack any pattern, i.e. appear random. The many applications of randomness have led to the development of several different methods for generating random data. Many of these have existed since ancient times, including dice, coin flipping, the shuffling of playing cards, the use of yarrow stalks (by divination) in the I Ching, and many other techniques. Because of the mechanical nature of these techniques, generating large amounts of sufficiently random numbers (important in statistics) required a lot of work and/or time. Thus, results would sometimes be collected and distributed as random number tables. Nowadays, after the advent of computational random number generators, a growing number of government-run lotteries, and lottery games, are using RNGs instead of more traditional drawing methods. RNGs are also used today to determine the odds of modern slot machines. Random number generators have applications in gambling, statistical sampling, computer simulation, cryptography, completely randomized design, and other areas where producing an unpredictable result is desirable. Random number generators are very useful in developing Monte Carlo method simulations as debugging is facilitated by the ability to run the same sequence of random numbers again by starting from the same random seed. They are also used in cryptography so long as the seed is secret. Sender and receiver can generate the same set of numbers automatically to use as keys. Some simple examples might be presenting a user with a "Random Quote of the Day", or determining which way a computer-controlled adversary might move in a computer game. Weaker forms of randomness are also closely associated with hash algorithms and in creating amortized searching and sorting algorithms. Some applications which appear at first sight to be suitable for randomization are in fact not quite so simple. For instance, a system that "randomly" selects music tracks for a background music system must only appear to be random, and may even have ways to control the selection of music; a true random system would have no restriction on the same item appearing two or three times in succession.
Inventory Simulation
While Inventory Optimization selects the mathematically optimal inventory levels, Inventory Simulation demonstrates “How” the inventory levels and policies will perform in the “real world” given real demand and supply variability. In business-oriented simulations, especially those involving quantitative techniques, it is often difficult to isolate the decision-making process from the mechanics of the simulation. This is particularly true with inventory simulations because of the amount of bookkeeping required for inventory management.
The Inventory Management Simulation (IMS), a computer-based simulation, is designed to alleviate this problem. It acts both as customer and bookkeeper for the student. It generates demands, and maintains all the necessary records. The student is then free to focus on individual decisions and the decision-making process. The interactive nature of the software makes the use of the simulation relatively unstructured, so the student can control the time and frequency of its use. The flexibility of the software allows the instructor to adapt it to a wide variety of learning situations
Common business challenges and business problem
- Optimized inventory levels not generating expected service performance
- Demand or supply distribution not reflective of real variability
- Highly volatile demand or seasonality
- Extended and variable supplier lead times
- Erratic fluctuations in inventory levels
- Inconsistent or low fill rates and increasing stock-outs
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